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The accumulation of small particles is analyzed in stationary flows through channels of variable width at small Reynolds number. The combined influence of pressure, viscous drag and thermal fluctuations is described by means of a…
This paper deals with optimal control problems described by a controlled version of Moreau's sweeping process governed by convex polyhedra, where measurable control actions enter additive perturbations. This class of problems, which…
We investigate the properties of highly compressible turbulence, the compressibility arising from a small effective polytropic exponent $\gamma_e$ due to cooling. In the limit of small $\gamma_e$, the density jump at shocks is shown to be…
Short-range repulsion governs the dynamics of matter from atoms to animals. Using theory, simulations, and experiments, we find that an ensemble of repulsive particles spreads compactly with a sharp boundary, in contrast to the diffusive…
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…
This paper addresses challenges in flexibly modeling multimodal data that lie on constrained spaces. Such data are commonly found in spatial applications, such as climatology and criminology, where measurements are restricted to a…
Compressible flow varies from ideal-gas behavior at high pressures where molecular interactions become important. Density is described through a cubic equation of state while enthalpy and sound speed are functions of both temperature and…
The linear theory for rotating compressible convection in a plane layer geometry is presented for the astrophysically-relevant case of low Prandtl number gases. When the rotation rate of the system is large, the flow remains geostrophically…
We formulate a control system model for the distributed flow of mixtures of highly heterogeneous gases through large-scale pipeline networks with time-varying injections of constituents, withdrawals, and control actions of compressors. This…
We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in…
Determining the Fourier representation of various molecular interactions is important for constructing density-based field theories from a microscopic point of view, enabling a multiscale bridge between microscopic and mesoscopic…
We establish the incompressible limit of weakly asymmetric simple exclusion processes coupled through particle collisions. The incompressible limit depends on various parameters in the particle system and is linked to fluid dynamics…
We study a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This model is compatible with continuum…
Consider two compressible immiscible fluids in 1D in the isentropic approximation. The first fluid is surrounded and in contact with the second one. As the Mach number of the first fluid vanishes, the coupled dynamics of the two fluids…
We revisit the problem of proving the incompressible limit for the compressible porous media equation with Newtonian drift and growth. The question is motivated by models of living tissues development including chemotaxis. We extend the…
We consider one-dimensional, locally finite interacting particle systems with two conservation laws. The models have a family of stationary measures with product structure and we assume the existence of a uniform bound on the inverse of the…
We study two new models of two particle species invading a surface from opposite sides. Collisions of particles of different species lead to the formation of congestion fronts. One of the models implements a reversible process whereas in…
The adsorption phenomenon of neutral particles from the limiting surfaces of the sample in the Langmuir approximation is investigated. The diffusion equation regulating the redistribution of particles in the bulk is assumed to be of…
This paper is concerned with the incompressible limit of the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions in R^N(N = 2, 3). It is rigorously shown that the local (and global) strong solution of the…
Motivated by recent interest in elastic problems in which the target space is non-Euclidean, we study a limit where local rest distances within an elastic body are incompatible, yet close to, distances within the ambient space.…